In this paper, we consider a criminal investigation on the collective guilt of part members in a working group. Assuming that the statistics we used are reliable, we present the Page Rank Model based on mutual information. First, we use the average mutual information between non-suspicious topics and the suspicious topics to score the topics by degree of suspicion. Second, we build the correlation matrix based on the degree of suspicion and acquire the corresponding Markov state transition matrix. Then, we set the original value for all members of the working group based on the degree of suspicion. At the last, we calculate the suspected degree of each member in the working group. In the small 10-people case, we build the improved Page Rank model. By calculating the statistics of this case, we acquire a table which indicates the ranking of the suspected degree. In contrast with the results given in this issue, we find these two results basically match each other, indicating the model we have built is feasible. In the current case, firstly, we obtain a ranking list on 15 topics in order of suspicion via Page Rank Model based on mutual information. Secondly, we acquire the stable point of Markov state transition matrix using the Markov chain. Then, we build the connection matrix based on the degree of suspicion and acquire the corresponding Markov state transition matrix. Last, we calculate the degree of 83 candidates. From the result, we can see that those suspicious are on the top of the ranking list while those innocent people are at the bottom of the list, representing that the model we have built is feasible. When suspicious topics and conspirators changed, a relatively good result can also be obtained by this model. In the current case, we have the evidence to believe that Dolores and Jerome, who are the senior managers, have significant suspicion. It is recommended that future attention should be paid to them. The Page Rank Model, based on mutual information, takes full account of the information flow in message distribution network. This model can not only deal with the statistics used in conspiracy, but also be applied to detect the infected cells in a biological network. Finally, we present the advantages and disadvantages of this model and the direction of improvements.

1. International Journal of Science and Engineering Applications
Volume 4 Issue 3, 2015, ISSN-2319-7560 (Online)
www.ijsea.com 100
Modified Page Rank Model in Investigation of
Criminal Gang
Ting LU
Research Center for Cloud Computing
North China University of Technology,
Beijing 100043, China
Qi Gao
Department of Mathematics,
Shandong Normal University,
Jinan 250002 China.
Xudong Wang
Department of Information System,
Shanghai University,
Shanghai 201800,China
Cong LIU
Department of Computer Science, Shandong
University of Science and Technology,
Qingdao 266590, China
Abstract:In this paper, we consider a criminal investigation on the collective guilt of part members in a working group. Assuming that
the statistics we used are reliable, we present the Page Rank Model based on mutual information. First, we use the average mutual info
rmation between non-suspicious topics and the suspicious topics to score the topics by degree of suspicion. Second, we build the correl
ation matrix based on the degree of suspicion and acquire the corresponding Markov state transition matrix. Then, we set the original v
alue for all members of the working group based on the degree of suspicion. At the last, we calculate the suspected degree of each me
mber in the working group. In the small 10-people case, we build the improved Page Rank model. By calculating the statistics of this c
ase, we acquire a table which indicates the ranking of the suspected degree. In contrast with the results given in this issue, we find thes
e two results basically match each other, indicating the model we have built is feasible. In the current case, firstly, we obtain a ranking
list on 15 topics in order of suspicion via Page Rank Model based on mutual information. Secondly, we acquire the stable point of Mar
kov state transition matrix using the Markov chain. Then, we build the connection matrix based on the degree of suspicion and acquire
the corresponding Markov state transition matrix. Last, we calculate the degree of 83 candidates. From the result, we can see that those
suspicious are on the top of the ranking list while those innocent people are at the bottom of the list, representing that the model we ha
ve built is feasible. When suspicious topics and conspirators changed, a relatively good result can also be obtained by this model. In th
e current case, we have the evidence to believe that Dolores and Jerome, who are the senior managers, have significant suspicion. It is
recommended that future attention should be paid to them. The Page Rank Model, based on mutual information, takes full account of t
he information flow in message distribution network. This model can not only deal with the statistics used in conspiracy, but also be ap
plied to detect the infected cells in a biological network. Finally, we present the advantages and disadvantages of this model and the dir
ection of improvements.
Keywords: Page Rank ;Markov Chain; Criminal Gangs; Biological Model; Algorithm; Markov Chain
1. INTRODUCTION
1.1 Background
With the advent of the information age, information technology
development has brought new challenges and opportunities to the
public security work. Because of its superiority, people are
paying close attention to how to integrate and reuse to the public
security data resources and how to achieve comprehensive
application of global data, the automatic association of all kinds
of information as well as the automatic mining function of a
variety of cues, which will provide integrated applications in the
information handling. Using the semantic network analysis and
the relevant models plays a major role in improving the
efficiency and accuracy of detection.
1.2 What is “Crime Gangs”?
Crime Gangs is a crime form, referring to the two or more
persons jointly committing one or more crimes. Intelligence
information (such as the collection of the relevant people’s
conversations in this given case) is the technical basis of the
intelligence analysis. The implementation of criminal
intelligence analysis is based on intelligence gathering, mining
and establishing crime patterns, analyzing and judging criminal
clues as well as a variety of relationships. Building an efficient
model to analyze the relevant information will surely provide
some useful clues for the detection of cases and the judgment of
criminal suspects.
1.3 The Mission of Our Team
In this paper, we would like to introduce the theory of
information analysis to solve the problems, which is described
as follows: In the previous case, it is our team’s duty to identify
the guilty parties among the 10 candidates. Similarly, the other
problem is to solve a relatively larger case, where there are
about 83 candidates.
The analysis and process of these problems are divided into
three steps. Firstly, we use the method of mutual information to
score all the topics mentioned. Secondly, we can acquire the
correlation matrix by calculating the score of the associated
topics among the candidates. Thirdly, by solving the Markov
Transfer Matrix, we get the stable point of Markov Transfer
Matrix, which is the final index of 83 candidates. By analyzing
this index, the 83 degree of suspicion can be determined.
2. PROBLEM ANALYSIS
2.1 Topics’ Suspicious Degree Analysis
First, we analyze the suspicious degree of talks between each
other, using the mutual information and entropy in information
theory, defined as M(A,B) = I(A) + I(B) - I(A,B), to obtain the

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scores of the 12 undetermined topics and the scores of
suspicious ones(Obviously, the scores of the suspicious are
supposed to be higher than the others). Further illustration is put
in models.
2.2 The Transmission of Suspicious Information in the
Working Group Analysis
The work group is divided into five parts, namely, the confirmed
suspects, the people with some suspicion, the undetermined
people and the innocent (listed by the degree of suspicion).
Because we refer to Google’s PangeRank algorithm, we need to
obtain the correlation matrix of this group of people first. Then
we can use this algorithm to get the Markov Transfer Matrix and
later get the stable points using the nature of Markov. The
acquisition of the correlation matrix is based on the message
topics among the 83 people. We can use gij to represent the total
scores of all the topics, thus getting an 83*83 correlation matrix.
2.3 The Initial Vector Distribution of the Working Group
Analysis
To solve the Markov stable point, we need to use the initial
vector distribution. We define the scores of the suspicious as α
(The total number of this group of people is n); the scores of the
innocent is 0; the scores of the undecided is β (The total number
of this group of people is m). They satisfy the equation nα + mβ
=1, and then we can decide the values of α and β through the
search of α with step size of 0.1
3. BASIC ASSUMPTIONS OF OUR
MODEL
3.1. All data is true and reliable.
3.2. There is valid evidence to prove the people who are
suspicious.
3.3. There is valid evidence to prove the people who are
innocent.
3.4. The suspicious topics have higher degree of doubt than that
of the undermined ones.
3.5. An objective and subjective attitude is kept in the process of
handling the cases.
3.6. These topics give a valid summary of the messages.
4. MODEL AND SOLUTION
Our whole model is divided into 3 parts, including 3.1, 3.2 and
3.3. In the 3.4 part, we use the whole model to analyze a simple
example. And in 3.5 and 3.6, we solve the real problem
presented in question 1, and its changed version in question 2.
4.1 Mutual Information Algorithm
Let me put a simple example to better illustrate this algorithm.
“What a good weather today! I would like to go fishing.” A
says to B. The words, such as “today”, “weather”, “good”, “I”,
“fishing” involved in this conversation, can be seen as key
words, and we can use 1 2, , , na a a to represent them.
When B says to A:“Yeah, really good weather! I will go
climbing.” Also, the words such as “weather”, “hiking”, “good”,
“I”, can be extracted as key words and we can use
1 2, , , mb b b to represent them. Here, we list the relationship
between the words of these two people.
Table 1: the language relationship table
A
today good fishing weather I
1 1 1 1 1 0 0
B weather I good climbing
0 0 0 1 1 1 1
Notes: “1” in the second row and second column of the table rep
resents the key word “today” said by A, but “0” in the fourth ro
w and second column represents that B didn’t say the key word
“1”indicates the value of mentioned topic in the chat,
“0”indicates the value of topic which is not mentioned in the
table.
We can use the formula of mutual information M(X,Y) = I(X) +
I(Y) - I(X,Y)to get the value of the mutual information, defined
as M(X,Y), where I(X) represents the entropy from A, I(Y)
represents the entropy from B.
0 0 1 1( ) log logI X P P P P   (4.1-1)
0 0 1 1( ) log logI Y P P P P   (4.1-2)
10 10 11 11 01 01( , ) log log logI X Y P P P P P P    (4.1-3)
P0 and P1 denoting the probability of 0 and 1 respectively; P10,
P11 and P01 denoting the probability of (1, 0), (1, 1) and (0, 1)
respectively.
4.2 Markov Chain Model
In order to get the Markov state transition matrix, we first need
to get the 83*83 Markov correlation matrix(rows represent the
person’s words, columns represent the words that others said to
him /her). According to each topic, sum up the weight of the
words involved in the conversation between one person and the
others so as to get the total weight of one person, in the same
way, we can come to the other people’s weight, thus getting an
83*83 Markov correlation matrix.
Although we use Google’s Page Rank model，some people are
not the information receivers in the case, so it is unavoidable
that the sum of a few columns in the association matrix is 0.
Taking this into account, when computing the Markov Transfer
Matrix, we do some special handling on the correlation matrix
to make the sum of all the columns of the correlation matrix
non-zero.
Define the Markov Transfer Matrix as ( )ijA a , then
'
j ij
i
c g  (4.2-1)
'
i ij
j
r g  (4.2-2)
Cj represents the sum of columns in matrix G(gij), ri represents
the sum of rows in matrix G(gij), gij represents the elements in
the correlation matrix G(gij).
The formula used to solve the elements in transfer matrix A is
'
(1 )
*
ij
ij
j
gd
a d
n c

  (4.2-3)
d is a model parameter, we choose to define d = 0.85 based on
experience. aij represents the summed scores of the message
topics involved in the conversation from person j to person i.
From the basic nature of the Markov chain, there is a stationary
distribution in the regular Markov chain 1 2( , , , )T
Nx x x x ,then
we can get the sorting in accordance with the conspiracy
possibility.
4.3 Improved Page Rank Model
As we have known，there are 7 conspirators among the 83
people in the second case and each person’s scores can be
defined as ( ), 1,2, ,7P i i  . And the scores of each
innocent person can be defined as P(j), j = 1,2,...,8. The model is
as follows:
7 8
1 1
max ( , ) ( ) ( )
i j
M s P i P j
 
   （4.3-1）

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. .st
Ax x （4.3-2）
1
1
n
i
i
x

 （4.3-3）
The objective function indicates the maximum probability gap
between the known conspirators and the innocent (All the
conspirators are put in the upper part of the list, and all
innocence in the lower part of the list, leaving the undecided
people located in the middle of the list). We use k to express the
maximum of mutual information in the 12 topics. 
represents the steps from the upper bound to 20. Through the
debugging and analysis, we find that when  is given a value
of 0.5, the results will be much more in line with the subject
requirements. s is the initial vector distribution, the
percentage of each conspirator is 0.1, and the percentage of each
innocent person equals to 0, so the undetermined equally
allocate the remaining percentage. We define that s ranges from
0.5 to 0.9 is distributed in steps of 0.1, and we can get an initial
vector distribution on the subject on the whole.
4.4 Solution of The 10-people Case
In practice, we conducted some exploratory analysis on the
previous case, and get 4 ranking list of the probability of all the
people when defining k =1，10，12，15，17，20，respectively.
Through comparative analysis, we find that when k=17, the
ranking we get will be more in line with the true outcome of the
case than other values, that is, people like Inez don't get off,
people like Carol are not falsely accused, and people like Bob
do not have the opportunity to get reduced sentences. When
k=17, we can obtain a ranking list of suspicious degree, listed as
follows:
Table 2：The Sorting Table of the degree of Suspicious (k=17)
Ranking Number Name
1 7 George
2 2 Bob
3 9 Inez
4 4 Dave
5 5 Ellen
6 1 Anne
7 8 Harry
8 10 Jaye
9 3 Carol
10 6 Fred
Conclusion Analysis:
(1)George and Dave are the given co-conspirators, ranking
fourth in the list. Meanwhile, Bob ranks second, illustrating he
is one of the co-conspirators, so he cannot get off. Inez ranks
third, meaning that we can also catch him.
(2)Jaye and Anne are both ranked relatively rearward, which is
in accordance with the given information. And based on Carol
ranking No.9, we can basically determine her innocence.
Overall, the solution derived from our models can meet the
actual requirements and have some promotional value.
From the previous analysis, we know that the 10-people case is
a microcosm of the current case, and the results of small case
subject has been given to us, so understanding and solving the
smaller case can be seen as a test of our models, which may help
us to modify them.
4.5 The Solution of the Current case for Problem 1
When conducting an exploratory analysis on the current case,
we used the same way as the first one to analyze. We found that
when k=17 or k=20, we can get two basically the same
probability rankings of all the people, much more in line with
the requirements listed in the subject.
First, we can obtain the ranking list of the 15 topics using the
Mutual Information Method.
Table 3：Score Ranking List of 15 Topics
Number Score
1 0.883016
2 0.857865
3 0.898072
4 0.87294
5 0.872976
6 0.857882
1 1
8 0.888021
9 0.883014
10 0.893037
11 1
12 0.888021
13 1
14 0.888034
15 0.883008
Notes: The numbers of suspicious topics are 7, 11, 13.
The suspicious degree ranking of the suspected, innocent and
the senior managers based on k=17.
Table4: The Sorting Table Based on the Suspicious Degree
of the Conspirators, Non-conspirators and Senior Managers (K=
17)
Ranking Name Number
1 Yao 68
2 Alex 22
4 Paul 44
6 Harvey 50
7 Dolores 11
8 Ulf 55
17 Jerome 17
19 Jean 19
27 Paige 3
28 Elsie 38
31 Darlene 49
46 Chris 1
57 Tran 65
58 Ellin 69
60 Gretchen 5

4. International Journal of Science and Engineering Applications
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Notes: The senior managers are Dolores, Jerome and Gretchen.
Conclusion Analysis:
(1) By analyzing the result, we can find that two senior
managers, namely Dolores and Jerome are both conspirators.
(2) The already known conspirators are shown in the forefront
of the ranking list, we can basically draw that they are the
conspirators.
(3)The already known non-conspirators are all at the rear of the
ranking list, except for Paige who ranks 27, the others can be
determined to be innocent. Although there are a few minor
differences, this result has been very much in line with the
actual situation, which means the feasibility and stability of the
model is very well.
4.6 The Solution of the Current Case for Problem 2
As to the second requirement, we can also use the Improved
Page Rank Model to analyze data. First obtain a modified
ranking list of the 15 topics, listed as follows:
Table 5：Score Ranking List of the 15 Modified Topics
number score
1 1
2 1.177737
3 1.20412
4 1.193429
5 1.172717
6 1.167063
7 1
8 1.199102
9 1.193429
10 1.20412
11 1
12 1.20412
13 1
14 1.173339
15 1.193429
Then we can get the ranking list about the suspicion degree of
the suspected, the innocent and the senior managers.
Table 6：The Sorting Table Based on the Suspicious Degree
of the Conspirators, Non-conspirators and Senior Managers
Number Name
1 Yao
2 Alex
4 Paul
6 Harvey
7 Dolores
8 Ulf
17 Jerome
19 Jean
27 Paige
28 Elsie
30 Darlene
45 Chris
57 Ellin
58 Tran
60 Gretchen
Notes: The senior managers are Dolores, Jerome and Gretchen,
the 7 suspected people are Yao, Alex, Paul, Harvey, Ulf, Elsie.
Conclusion Analysis
The newly added conspirator Chris does not make much
difference in results compared with the ones in the first
requirement. According to analysis, this may be due to Chris's
inactive involvement in the conversation, so even if he is one of
the conspirators, his influence on others is very weak, resulting
in the basically similar results.
4.7 The Solution of the Current Case for Problem 3
In this section, we introduce the conception of Semantic
network and apply the theory of Similarity to the calculation of
topic scores.
As we have obtained the original messages, which is a much
bigger corpus than that we used in the first two questions, so we
can apply the similarity analyze into our model. To describe it in
detail:
First: Calculate the similarities of among the 3 suspected
messages(A) and the 12 unsuspected messages (B),
A includes A1，A2，A3，B includes，
( , )i jSim A B
d




（4.7-1）
d : the distance between the two corpus.
 : an changeable parameter.(usually between 0 and 1)
Second: give the index rank of B1，B2，……，B12
12
1
( , ),( 1,2,3)j i j
j
B Sim A B i

  （4.7-2）
Third: set the value of A1，A2，A3.
( ),( 1,2,3 1....12)i jA Max B i j   （4.7-3）
So far, we successfully obtain the rank of the 15 messages,
comparing with the rank based on the index of mutual
information; this model theoretically provides a more credible
result.
5. ADVANTAGES AND
DISADVANTAGES
5.1 Advantages:
We introduced the concept of mutual information when
computing topics, and build the relationship between the
suspicious topics and the undetermined ones.
5.2 Disadvantages:
●As it is mentioned in requirement 3 that due to the
limitation of the message traffic, we can just roughly determine
the doubt degree of the topics by semantic network analysis.
● Though the computing of the mutual information, we
can just determine the values of the 12 undetermined topics,
however, the values of the 3 higher suspected ones are
artificially assigned.
●Without much experience for reference in the model, the
accuracy of the results may be undermined.

5. International Journal of Science and Engineering Applications
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6. PROMOTION OF THE MODEL
Through the analysis, we found that our model is considerable
promotional, such as being used as a method to find the infected
or diseased cells in a biological network. Briefly speaking, if we
can get the meaningful characteristics from all the cells can
calculate the mutual information between these characteristics.
Later, we can try to obtain the mutual information between the
undetermined cells and the infected ones so as to get the
probability ranking list of the undetermined. Though the
detecting process, we may us the Improved Search-based Page
Rank Model and the Markov Transfer Matrix to simplify our
operation as well as increase the validity of our research.
We have introduced the mutual information theory in analyzing
this problem in the first two parts, with a relatively satisfactory
result. As far as we know, semantic network analysis which is a
widely used in artificial intelligence and computational
linguistics. It provides a structure and process for reasoning
about knowledge or language. And another useful computational
linguistics capability in natural language processing is text
analysis.
7. CONCLUSION
In this paper, we introduce the model of improved Page Rank
algorithm based on mutual information and successfully solved
the case problems. The consequences are listed as follows: In
the previous case, George and Dave are the given
co-conspirators. Bob and Inez are proved other co-conspirators.
Carol is innocent. Overall, the solution derived from our models
can meet the actual requirements and have some promotional
value. Then in the next case, by analyzing the result, we can find
that two senior managers, namely Dolores and Jerome are both
conspirators. This will help the investigation of the cases. The
other version of the second case, the newly added suspect Chris
does not make much difference in results compared with the
ones in the first requirement. According to analysis, this may be
due to Chris's inactive involvement in the conversation, so even
if he is one of the conspirators, his influence on others is very
weak, resulting in the basically similar results.
All in all, as we only use the topics which are derived from
original messages in mutual information analysis, so our result
will be more valid if we have a larger corpus. That is to say, we
can introduce semantic network and use similarity-computing to
acquire a more precise result, in that way, our judgment will be
more reasonable.
8. ACKNOWLEDGMENTS
This work was supported in part by the Graduate Innovation
Foundation Project of Shan-dong University of Science and
Technology (YC140106). Also, we would like to thank those
anonymous reviewers for their constructive comments to help us
improve the paper.
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[3]Terry. (1999) The Page Rank Citation Ranking: Bringing
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[4]Jackendoff, Ray S.(1972) Semantic Interpretation in
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[5]Xing, W., Ghorbani A. (2004) Weighted Page Rank algorithm,
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[7]John F. Sowa (1991) Principles of Semantic Networks.
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